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Question

Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

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Solution

Given, speed of water flow =10 m/min=1000 cm/min

Radius of the pipe =510×2=0.25 cm

Area of the face of pipe =πr2=227×(0.25)2=0.1964 cm2

Also, given diameter of the conical vessel =40 cm

Radius of the conical vessel =402=20 cm

And depth of the conical vessel =24 cm

Volume of the conical flask =13πr2h=13×227×(20)2×24=21120021=10057.14 cm3
Required time to fill the conical flask =Volume of the conical vesselArea of the face of pipe×Speed of water

=10057.140.1964×10×100

=51.20 min=51 min+20100×60 s=51 min 12 s


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